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where s is the semi-perimeter:
The formula is named after Hero of Alexandria or Heron of Alexandria, who was a Greek mathematician and engineer and lived in the ancient city of Alexandria, in Roman Egypt, around 10AD - 70AD. He proved his formula in his book Metrica, written around 60AD.
Heron's formula usage example
Problem: Given the sides of a triangle, a = 4, b = 13, c = 15 find the area of a triangle.
- Find the semi-perimeter: s = (a+b+c)/2 = (4+13+15)/2=16
- Find the area as square root of 16*(16-4)*(16-13)*(16-15) = 16*12*3*1 = 576. The square root of 576 is 24.
Here is how you should enter the example into the calculator above: Area of a triangle using Heron's formula